Did people in Seoul also use the expression "going downtown" 20 years ago?

I'm watching the streaming version of the sitcom "Live Right," which aired 2-3 years ago (sic),
and Hyung-wook, Noh Ju-hyun's son, asks his older sisters for some pocket money so he can "go downtown."
Since I'm originally from Busan, I've mostly used the expression "going to Seomyeon."